LOWER BOUNDS ON LP QUASI‐NORMS AND THE UNIFORM SUBLEVEL SET PROBLEM

Recently, Steinerberger proved a uniform inequality for the Laplacian serving as a counterpoint to the standard uniform sublevel set inequality which is known to fail for the Laplacian. In this paper, we observe that many inequalities of this type follow from a uniform lower bound on the $L^1$ norm, and give an analogous result for any linear differential operator, which can fail for non-linear operators. We consider lower bounds on the $L^p$ quasi-norms for $p
42 pages, 1 figure, supersedes arXiv:2005.09407: main theorems strengthened and surrounding discussion presented in a much different context